Problem: Simplify the following expression: $\dfrac{12r}{15r^2}$ You can assume $r \neq 0$.
Answer: $ \dfrac{12r}{15r^2} = \dfrac{12}{15} \cdot \dfrac{r}{r^2} $ To simplify $\frac{12}{15}$ , find the greatest common factor (GCD) of $12$ and $15$ $12 = 2 \cdot 2 \cdot 3$ $15 = 3 \cdot 5$ $ \mbox{GCD}(12, 15) = 3 $ $ \dfrac{12}{15} \cdot \dfrac{r}{r^2} = \dfrac{3 \cdot 4}{3 \cdot 5} \cdot \dfrac{r}{r^2} $ $\phantom{ \dfrac{12}{15} \cdot \dfrac{1}{2}} = \dfrac{4}{5} \cdot \dfrac{r}{r^2} $ $ \dfrac{r}{r^2} = \dfrac{r}{r \cdot r} = \dfrac{1}{r} $ $ \dfrac{4}{5} \cdot \dfrac{1}{r} = \dfrac{4}{5r} $